Bounded and Unbounded Function

Let a function be defined as f(x): A → B and we can find two real numbers m and M such that m < f(x) < M ∀ x ε A then f(x) is called the bounded function. m and M are called the lower-bound and the upper-bound of f(x) respectively. The range of f(x) is [m, M] (see figure given below), If however, m and M or either of them is not defined (i.e. infinite) then f(x) is said to be unbounded function.

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